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 Go to latest Published: Jun 15, 2021 License: MIT Imports: 1 Imported by: 0

Documentation

Index

Constants

This section is empty.

Variables

View Source 
var A = FieldElement{
	486662, 0, 0, 0, 0, 0, 0, 0, 0, 0,
}

A is a constant in the Montgomery-form of curve25519.

View Source 
var SqrtM1 = FieldElement{
	-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482,
}

SqrtM1 is the square-root of -1 in the field.

Functions

func ExtendedGroupElementCMove 

func ExtendedGroupElementCMove(t, u *ExtendedGroupElement, b int32)

func ExtendedGroupElementCopy 

func ExtendedGroupElementCopy(t, u *ExtendedGroupElement)

func FeAdd 

func FeAdd(dst, a, b *FieldElement)

func FeCMove 

func FeCMove(f, g *FieldElement, b int32)

Replace (f,g) with (g,g) if b == 1; replace (f,g) with (f,g) if b == 0.

Preconditions: b in {0,1}.

func FeCombine 

func FeCombine(h *FieldElement, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64)

func FeCompare 

func FeCompare(x, y *[32]byte) int

func FeCopy 

func FeCopy(dst, src *FieldElement)

func FeFromBytes 

func FeFromBytes(dst *FieldElement, src *[32]byte)

func FeInvert 

func FeInvert(out, z *FieldElement)

func FeIsNegative 

func FeIsNegative(f *FieldElement) byte

func FeIsNonZero 

func FeIsNonZero(f *FieldElement) int32

func FeIsequal 

func FeIsequal(f, g FieldElement) int

func FeMontgomeryXToEdwardsY 

func FeMontgomeryXToEdwardsY(out, x *FieldElement)

compare to fe_montx_to_edy

func FeMul 

func FeMul(h, f, g *FieldElement)

FeMul calculates h = f * g Can overlap h with f or g.

Preconditions: 

|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
|g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.

Postconditions: 

|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

Notes on implementation strategy:

Using schoolbook multiplication. Karatsuba would save a little in some cost models.

Most multiplications by 2 and 19 are 32-bit precomputations; cheaper than 64-bit postcomputations.

There is one remaining multiplication by 19 in the carry chain; one *19 precomputation can be merged into this, but the resulting data flow is considerably less clean.

There are 12 carries below. 10 of them are 2-way parallelizable and vectorizable. Can get away with 11 carries, but then data flow is much deeper.

With tighter constraints on inputs, can squeeze carries into int32.

func FeNeg 

func FeNeg(h, f *FieldElement)

FeNeg sets h = -f

Preconditions: 

|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

Postconditions: 

|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

func FeOne 

func FeOne(fe *FieldElement)

func FePow22523 

func FePow22523(out, z *FieldElement)

func FeSquare 

func FeSquare(h, f *FieldElement)

FeSquare calculates h = f*f. Can overlap h with f.

Preconditions: 

|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.

Postconditions: 

|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

func FeSquare2 

func FeSquare2(h, f *FieldElement)

FeSquare2 sets h = 2 * f * f

Can overlap h with f.

Preconditions: 

|f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.

Postconditions: 

|h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.

See fe_mul.c for discussion of implementation strategy.

func FeSub 

func FeSub(dst, a, b *FieldElement)

func FeToBytes 

func FeToBytes(s *[32]byte, h *FieldElement)

FeToBytes marshals h to s. Preconditions: 

|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

Write p=2^255-19; q=floor(h/p). Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).

Proof: 

Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.

Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
Then 0<y<1.

Write r=h-pq.
Have 0<=r<=p-1=2^255-20.
Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.

Write x=r+19(2^-255)r+y.
Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.

Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.

func FeZero 

func FeZero(fe *FieldElement)

func GeAdd 

func GeAdd(r, a, b *ExtendedGroupElement)

GeAdd sets r = a+b. r may overlaop with a and b.

func GeDouble 

func GeDouble(r, p *ExtendedGroupElement)

func GeDoubleScalarMultVartime 

func GeDoubleScalarMultVartime(r *ProjectiveGroupElement, a *[32]byte, A *ExtendedGroupElement, b *[32]byte)

GeDoubleScalarMultVartime sets r = a*A + b*B where a = a[0]+256*a[1]+...+256^31 a[31]. and b = b[0]+256*b[1]+...+256^31 b[31]. B is the Ed25519 base point (x,4/5) with x positive.

func GeIsNeutral 

func GeIsNeutral(p *ExtendedGroupElement) bool

GeIsNeutral returns 1 if p is the neutral point returns 0 otherwise

func GeNeg 

func GeNeg(r *ExtendedGroupElement, p ExtendedGroupElement)

func GeScalarMult 

func GeScalarMult(r *ExtendedGroupElement, a *[32]byte, A *ExtendedGroupElement)

GeScalarMult sets r = a*A where a = a[0]+256*a[1]+...+256^31 a[31].

func GeScalarMultBase 

func GeScalarMultBase(h *ExtendedGroupElement, a *[32]byte)

GeScalarMultBase computes h = a*B, where 

a = a[0]+256*a[1]+...+256^31 a[31]
B is the Ed25519 base point (x,4/5) with x positive.

Preconditions: 

a[31] <= 127

func HashToEdwards 

func HashToEdwards(out *ExtendedGroupElement, h *[32]byte)

HashToEdwards converts a 256-bit hash output into a point on the Edwards curve isomorphic to Curve25519 in a manner that preserves collision-resistance. The returned curve points are NOT indistinguishable from random even if the hash value is. Specifically, first one bit of the hash output is set aside for parity and the rest is truncated and fed into the elligator bijection (which covers half of the points on the elliptic curve).

func PreComputedGroupElementCMove 

func PreComputedGroupElementCMove(t, u *PreComputedGroupElement, b int32)

func ScCMove 

func ScCMove(f, g *[32]byte, b int32)

ScCMove is equivalent to FeCMove but operates directly on the [32]byte representation instead on the FieldElement. Can be used to spare a FieldElement.FromBytes operation.

func ScClamp 

func ScClamp(a *[32]byte)

ScClamp Sets and clears bits to make a random 32 bytes into a private key

func ScMinimal 

func ScMinimal(scalar *[32]byte) bool

ScMinimal returns true if the given scalar is less than the order of the curve.

func ScMulAdd 

func ScMulAdd(s, a, b, c *[32]byte)

Input: 

a[0]+256*a[1]+...+256^31*a[31] = a
b[0]+256*b[1]+...+256^31*b[31] = b
c[0]+256*c[1]+...+256^31*c[31] = c

Output: 

s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
where l = 2^252 + 27742317777372353535851937790883648493.

func ScNeg 

func ScNeg(b, a *[32]byte)

ScNeg computes: b = -a (mod l) 

where l = 2^252 + 27742317777372353535851937790883648493.

func ScReduce 

func ScReduce(out *[32]byte, s *[64]byte)

Input: 

s[0]+256*s[1]+...+256^63*s[63] = s

Output: 

s[0]+256*s[1]+...+256^31*s[31] = s mod l
where l = 2^252 + 27742317777372353535851937790883648493.

Types

type CachedGroupElement 

type CachedGroupElement struct {
	Z, T2d FieldElement
	// contains filtered or unexported fields
}

type CompletedGroupElement 

type CompletedGroupElement struct {
	X, Y, Z, T FieldElement
}

func (*CompletedGroupElement) ToExtended 

func (p *CompletedGroupElement) ToExtended(r *ExtendedGroupElement)

func (*CompletedGroupElement) ToProjective 

func (p *CompletedGroupElement) ToProjective(r *ProjectiveGroupElement)

type ExtendedGroupElement 

type ExtendedGroupElement struct {
	X, Y, Z, T FieldElement
}

func (*ExtendedGroupElement) Double 

func (p *ExtendedGroupElement) Double(r *CompletedGroupElement)

func (*ExtendedGroupElement) FromBytes 

func (p *ExtendedGroupElement) FromBytes(s *[32]byte) bool

func (*ExtendedGroupElement) FromParityAndY 

func (p *ExtendedGroupElement) FromParityAndY(bit byte, y *FieldElement) bool

func (*ExtendedGroupElement) ToBytes 

func (p *ExtendedGroupElement) ToBytes(s *[32]byte)

func (*ExtendedGroupElement) ToCached 

func (p *ExtendedGroupElement) ToCached(r *CachedGroupElement)

func (*ExtendedGroupElement) ToProjective 

func (p *ExtendedGroupElement) ToProjective(r *ProjectiveGroupElement)

func (*ExtendedGroupElement) Zero 

func (p *ExtendedGroupElement) Zero()

type FieldElement 

type FieldElement [10]int32

FieldElement represents an element of the field GF(2^255 - 19). An element t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on context.

type PreComputedGroupElement 

type PreComputedGroupElement struct {
	// contains filtered or unexported fields
}

func (*PreComputedGroupElement) Zero 

func (p *PreComputedGroupElement) Zero()

type ProjectiveGroupElement 

type ProjectiveGroupElement struct {
	X, Y, Z FieldElement
}

func (*ProjectiveGroupElement) Double 

func (p *ProjectiveGroupElement) Double(r *CompletedGroupElement)

func (*ProjectiveGroupElement) ToBytes 

func (p *ProjectiveGroupElement) ToBytes(s *[32]byte)

func (*ProjectiveGroupElement) Zero 

func (p *ProjectiveGroupElement) Zero()

Source Files

View all Source files

Directories

Path Synopsis
groth16
bls12381
bn256
bn256/utils/bn254
bn256/utils/bn254/bls

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